The lip idea that you mentioned, could be applied to this, a box with no lid sort of thing could be made on the driver station, into which the laptop could simply sit( with holes for USB, charging etc.)
Another alternative non-adhesive method, would be to use a piece of cordage, which would go around the hinges( the things with join the screen and the non-important bit with the keyboard
). Two brackets could be used which fit over the front corners of the laptop( but this is really dangerous, because if you close your screen it might crack)
Also this sort of breaks the non-adhesive rule, but you could attach little squares of the double sided tape included in the KOP to each of the little rubber feet on your laptop( if it has them) and then mount it the the console that way( that stuff is strong)
You guys have probably already crated and sent your Robot for the Australia Regional, so you'd have to make something which you could take with you on the plane